Question

Population of Delhi increases by $10$% every year. If the current population of Delhi is $1,331,000$ then what was its population $3$ years ago?

• A. $1000000$
• B. $25000$
• C. $10000000$
• D. $1543200$

Answer 1

Answer: (A)

$1000000$

Let the population 3 years ago be ${}^{\prime }{x}^{\prime }$

Let the population 2 years ago be ${}^{\prime }{y}^{\prime }$

So by increasing the population 3 years ago by $10\%$

$\Rightarrow y=x+\frac{10}{100}\times x$

$=\frac{11x}{10}$

Let us assume the population 1 year ago as ${}^{\prime }{z}^{\prime }$

By increasing the population 2 years ago by $10\%$

$\Rightarrow z=y+\frac{10}{100}\times y$

$=\frac{11y}{10}$

Substitute the value of $y$

$\Rightarrow z=\frac{11}{10}(\frac{11x}{10})$

$=\frac{121x}{100}$

Let us assume the current population as ${}^{\prime }{p}^{\prime }$

By increasing the population 1 year ago by $10\%$

$\Rightarrow p=z+\frac{11}{10}\times z$

$=\frac{11z}{10}$

Given: Present population $=1,331,000$

Substituting the values of ${}^{\prime }{z}^{\prime }$ and ${}^{\prime }{p}^{\prime }$

$\Rightarrow 1331000=\frac{11}{10}(\frac{121x}{100})$

$\Rightarrow x=\frac{1331000\times 1000}{1331}$

$\Rightarrow x=100000$

$\therefore$ Population of Delhi 3 years ago $1000000$